Wawrinka mastered former finalist Tsonga in straight sets to reach his third Australian Open semifinal after a mid-match argument on Tuesday.
The world number four won 7-6 (7/2), 6-4, 6-3 in two hours, 15 minutes for his eighth Grand Slam semifinal appearance.
It puts the three-time Grand Slam champion, the winner in Melbourne in 2014, just one victory away from his fourth Slam final.
"It's not easy to play against him. He's a strong player," Wawrinka said of Tsonga.
"I think (the) conditions were quite fast today. It was a bit windy. Not easy to control (the ball).
"I started to move a bit better and be a bit more aggressive from the first shot. I think that's what made the difference."
It was a consummate performance from Wawrinka, with three service breaks from three break points, hitting 41 winners, 21 of them on the forehand, and just 28 unforced errors.
Yet there were some tense moments between the two with an extraordinary squabble breaking out after Wawrinka took the opening set in a tiebreaker.
During the terse conversation in French, Wawrinka was heard to tell Tsonga, "You're the one who's looking and talking to me" and then, "Relax, it's just a tennis match."
The interchange follows an incident at the 2014 Davis Cup final when the French team confronted Wawrinka over a comment he made during Switzerland's victory in Lille.
Wawrinka will now face his compatriot Roger Federer after he powered into the semifinals with a dominant straight-sets win over Germany's Mischa Zverev, who previously beat world number one Andy Murray in the round of 16.
The 17-time Grand Slam champion extended his record for most Australian Open semifinal appearances to 13 with his victory.
It will also be a record-stretching 41st Grand Slam semifinal for the Swiss legend.
"I'm happy. I played as well as I could in this tournament. I never thought I would be this good. Here I am still standing in a semifinal to play Stan," Federer said on court.
"It couldn't be cooler for the both of us. I can't wait.
"I thought (pre-tournament) I might win a few rounds, depending on the draw, maybe fourth round or quarters. That was my call."
It was a dominant performance from the 35-year-old Federer, hitting 65 winners to just 13 unforced errors and breaking the serve-volleyer Zverev's serve six times.
Zverev, ranked 50, had brought off one of the major upsets of the tournament with a fourth-round win over Murray and didn't play badly against Federer, making only 13 unforced effors.
Federer has Swiss Davis Cup team-mate Wawrinka standing in his way for a place in Sunday's final. He leads Wawrinka 18-3.